here is a problem i am trying to do.
where is nth Fibonacci number. following is my attempt to prove.
let m be arbitrary in N. so the goal is
where k runs in N.so let n be arbitrary in N. suppose
since we have to prove P(n), suppose
I have proven some base cases for n=0,1,2 so the next case is
so using inductive hypothesis, it follows that
we can also come up the following conclusion for n-1,
but I don't know what to do with this. I thought of another approach. since I assumed that
I can use this for the inductive hypothesis , but I can't be sure if
because since m is arbitrary in N,m could be zero, in which case the above inequality fails.
So what approach should I take here ?